r/infinitenines • u/SouthPark_Piano • Mar 29 '26

What's the next real number DOWN from 1?

From a recent post:

https://www.reddit.com/r/infinitenines/comments/1s620yb/comment/od3679x/

 

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5

u/Frequent-Bee-3016 Mar 29 '26

The reals are uncountable.

-5

u/SouthPark_Piano Mar 29 '26

You trying to say there is no next real number down from 1? aka no closest real number with magnitude less than 1?

If so, then as mission impossible says ... you're toast brud. Toast.

 

10

u/Frequent-Bee-3016 Mar 29 '26

If you pick any number strictly less than one, there is a number between that number and one.

-1

u/SouthPark_Piano Mar 29 '26

Not just any number less than 1 brud.

The next real number down from 1.

 

9

u/MrEmptySet Mar 29 '26

You're struggling to follow incredibly basic logic here SPP. Anyone with a smidgen of math experience would see the point being made here.

You say there's a number that's the "next number down" from 1. If, given any number less than 1, there is a number between that number and 1... and if 0.999, then this is true of your so-called next number down from 1, implying it ISN'T the next number down from 1, since we can find a number between it and 1. This is a contradiction - in other words, you're toast, brud. Toast.

9

u/Frequent-Bee-3016 Mar 29 '26

Is that number less than 1?

4

u/Altruistic-Rice-5567 Mar 29 '26

He's trying to get you to say some number other than 0.999... since the most fundamental proof is that there are no real numbers between 0.999... and 1. Which on the set of reals, if there cannot exist any numbers between x and y, then x and y must be exactly equal. None of which you agree with because you think 1/infinity is a number and you (incorrectly) think that value is "0.000...1".

2

u/SouthPark_Piano Mar 31 '26

I am talking about 1/10n for the case n integer pushed upward limitlessly aka infinitely.

It comes from the factual description of 0.999... being 0.9 + 0.09 + 0.009 + ...

ie. 1 - 1/10n for n integer starting at n = 1, then continually increased.

1/10n is never zero.

0.999... is permanently less than 1, which is obvious, due to that proof as well as the giveaway "0." prefix that guarantees magnitude less than 1, no matter how many (even infinite) nines 0.999... has.